Question

Sam has just got engaged and wants to pay for her celebration in 18 months from now. She has decided that she wants to start saving for the wedding today. She transferred $1,000 to her TFSA for the wedding and also established a directed debit of $300 to her TFSA at the end of each month. The TFSA pays interest monthly at 2.5%. a) How much money will she have saved for the wedding in 18 months from now? b) She decides to change her direct debit from the end of the month, to the start of each month. How much extra will she earn from this?

Answer 1

Part A:

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

FV of Annuity :

Annuity is series of cash flows that are deposited at regular intervals for specific period of time. Here deposits are made at the end of the period. FV of annuity is future value of cash flows deposited at regular intervals grown at specified int rate or Growth rate to future date.

FV of Annuity = CF [ (1+r)^n - 1 ] / r
r - Int rate per period
n - No. of periods

FV of $ 1000 deposited Today:

Particulars	Amount
Present Value	$            1,000.00
Int Rate	0.2083%
Periods	18

Future Value = Present Value * ( 1 + r )^n
= $ 1000 ( 1 + 0.002083) ^ 18
= $ 1000 ( 1.002083 ^ 18)
= $ 1000 * 1.0382
= $ 1038.17

FV of Annuity of $ 300 deposited at the end of Month:

Particulars	Amount
Cash Flow	$               300.00
Int Rate	0.208%
Periods	18

FV of Annuity = Cash Flow * [ [ ( 1 + r ) ^ n ] - 1 ] /r
= $ 300 * [ [ ( 1 + 0.00208 ) ^ 18 ] - 1 ] / 0.00208
= $ 300 * [ [ ( 1.002083 ) ^ 18 ] - 1 ] / 0.002083
= $ 300 * [ [1.0382] - 1 ] / 0.002083
= $ 300 * [0.0382] /0.002083
= $ 5496.7

Amount in Account after 18 Months = $ 1038.17 + $ 5496.70

= $ 6534.87

Part B:

Future Value:

Future Value is Value of current asset at future date grown at given int rate or growth rate.

FV = PV (1+r)^n
Where r is Int rate per period
n - No. of periods

FV of $ 1000 deposited Today:

Particulars	Amount
Present Value	$            1,000.00
Int Rate	0.2083%
Periods	18

Future Value = Present Value * ( 1 + r )^n
= $ 1000 ( 1 + 0.002083) ^ 18
= $ 1000 ( 1.002083 ^ 18)
= $ 1000 * 1.0382
= $ 1038.17

FV of Annuity of $ 300 deposited at the begining of Month:

Particulars	Amount
Cash Flow	$         300.00
Int Rate	0.208%
Periods	18

FV of Annuity Due = ( 1+ r) [ Cash Flow * [ [ ( 1 + r )^n ] - 1 ] /r ]
= ( 1 + 0.0021 ) * [300 * [ [(1+0.0020833)^18] - 1 ] / 0.0020830 ]
= ( 1.0021 ) * [300 * [ [( 1.0021 ) ^ 18 ] - 1 ] / 0.0020833 ]
= ( 1.0021 ) * [300 * [ [ 1.0382 ] - 1 ] / 0.0020833 ]
= ( 1.0021 ) * [ $ 5496.7 ]
= $ 5508.15

Amount in Account after 18 Months = $ 1038.17 + $ 5508.15

= $ 6546.32

Extra Amount earned is $ 6546.32 - $ 6534.87

= $ 11.45